z²=3+4i 求z的模
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z=x+yi
z^2 =3+4i
(x^2-y^2)+ (2xy)i = 3+4i
=>
x^2-y^2 =3 (1)
y^2 =4 (2)
sub (2) into (1)
x^2 -4 =3
x^2 = 1 or -1
from (2)
y= 2 or -2
z = 1+2i or 1-2i or -1+2i or -1-2i
|z|=√5
z^2 =3+4i
(x^2-y^2)+ (2xy)i = 3+4i
=>
x^2-y^2 =3 (1)
y^2 =4 (2)
sub (2) into (1)
x^2 -4 =3
x^2 = 1 or -1
from (2)
y= 2 or -2
z = 1+2i or 1-2i or -1+2i or -1-2i
|z|=√5
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